Question

Retirement of debt. (Tables needed.) Steve Milner borrowed $120,000 on July 1, 2017. This amount plus accrued interest at 8% compounded semiannually is to be repaid in total on July 1, 2027. To retire this debt, Milner plans to contribute to a debt retirement fund five equal amounts starting on July 1, 2022 and continuing for the next four years. The fund is expected to earn 6% per annum.

Instructions Compute how much must be contributed each year by Steve Milner to provide a fund sufficient to retire the debt on July 1, 2027?

Answer 1

Date	Opening Amount($)	Interest@4% for 6 months($)	Closing Amount($) (Opening+Interest)
July1,2017	120,000	120000*4% = 4,800	124,800
January1,2018	124,800	124800*4% = 4,992	129,792
July1,2018	129,792	129792*4% = 5,192	134,984
January1,2019	134,984	134984*4% = 5,400	140,384
July1,2019	140,384	140384*4% = 5,615	146,000
January1,2020	146,000	5,840	151,840
July1,2020	151,840	6,074	157,914
January1,2021	157,914	6,317	164,231
July1,2021	164,231	6,569	170,800
January1,2022	170,800	6,832	177,632
July1,2022	177,632	7,105	184,737
January1,2023	184,737	7,389	192,126
July1,2023	192,126	7,685	199,811
January1,2024	199,811	7,992	207,803
July1,2024	207,803	8,312	216,115
January1,2025	216,115	8,645	224,760
July1,2025	224,760	8,990	233,750
January1,2026	233,750	9,350	243,100
July1,2026	243,100	9,724	252,824
January1,2027	252,824	10,113	262,937

He will repay $262,937 at july1, 2027.

Milner plans to contribute to a debt retirement fund five equal amounts starting on July 1, 2022 and continuing for the next four years. So five equal installments ended on July 1, 2026. But we will repay Borrowed amount on July1, 2027. So the amount on July1, 2017 to be converted to amount on July1, 2016 with present value formula.

Future value / (1+interest rate)^1 = Present value

Therefore, Future value is $262,937

$262,937 / (1+0.06)^1 = $248,054

Calculation of amount to be contributed each year by Steve Milner to provide a fund sufficient to retire the debt on July 1, 2027.

We know the Future value of Annuity = Amount to be invested every year{ ( 1+Interest rate)^n - 1 }/ Interest rate

We also know the Future value amount is equal to $248,052

There fore Amount to be invested = $248,052 / {(1+0.06)^5 - 1) / 0.06}

There fore amount to be invested every year from July1, 2022 is $44,004. to retire the debt on July 1, 2027